A numerical model of stress driven grain boundary diffusion

Journal of Computational Physics

Volumn 193, Issue 1, 2004, Pages 275-305

  Sethian, J A ^a   Wilkening, John ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

Corner singularity; Elasticity; Electromigration; Finite element method; Grain boundary

Indexed keywords

CONTINUUM MECHANICS; DIFFUSION; ELECTROMIGRATION; FINITE ELEMENT METHOD; GRAIN BOUNDARIES; MICROELECTRONICS; STRESSES;

BASE FUNCTION; CONTINUUM MODEL; CORNER SINGULARITY; DIFFUSION PROBLEMS; GRAIN BOUNDARY NETWORK; GRAIN-BOUNDARIES; GRAIN-BOUNDARY DIFFUSION; MICROELECTRONIC CIRCUITS; STRESS FIELD; TRANSPORT PHENOMENON;

ELASTICITY;

EID: 0344550358     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2003.08.015     Document Type: Article

References (33)

1. P.S. Ho, T. Kwok, Electromigration in metals, Rep. Prog. Phys. 52 (1989) 301-348.
2. K.-N. Tu, J.W. Mayer, L.C. Feldman, Electronic Thin Film Science for Electrical Engineers and Materials Scientists, Macmillan, New York, 1992.
3. W.W. Mullins, Mass transport at interfaces in single component systems, Metall. Mater. Trans. A 26 (8) (1995) 1917-1929.
4. M. Schimschak, J. Krug, Electromigration-induced breakup of two-dimensional voids, Phys. Rev. Lett. 80 (8) (1998) 1674-1677.
5. Z. Li, H. Zhao, H. Gao, A numerical study of electro-migration voiding by evolving level set functions on a fixed cartesian grid, J. Comput. Phys. 152 (1999) 281-304.
6. A. Averbuch, M. Israeli, I. Ravve, I. Yavneh, Computation for electro-migration in interconnects of micro-electronics devices, J. Comput. Phys. 167 (2001) 316-371.
7. A.C.F. Cocks, S.P.A. Gill, A variational approach to two dimensional grain growth I. Theory, Acta Mater. 44 (12) (1996) 4765-4775.
8. D. Moldovan, D. Wolf, S.R. Phillpot, A. Haslam, Mesoscopic simulations of two-dimensional grain growth with anisotropic grain-boundary properties, Philos. Magn. A 82 (7) (2002) 1271-1297.
9. A.J. Haslam, D. Moldovan, S.R. Phillpot, D. Wolf, H. Gleiter, Atomistic and mesoscale simulation of grain growth in nanocyrstalline thin films, Comput. Mater. Sci. 23 (2002) 15-32.
10. M.C. Demirel, A.P. Kuprat, D.C. George, A.D. Rollett, Bridging simulations and experiments in microstructure evolution, Phys. Rev. Lett. 90 (1) (2003) 016106.
11. R. Kirchheim, Stress and electromigration in Al-lines of integrated circuits, Acta Metall. Mater. 40 (2) (1992) 309-323.
12. M.A. Korhonen, P. Borgesen, K.N. Tu, C.-Y. Li, Stress evolution due to electromigration in confined metal lines, J. Appl. Phys. 73 (8) (1993) 3790-3799.
13. A.F. Bower, D. Craft, Analysis of failure mechanisms in the interconnect lines of microelectronic circuits, Fatigue Fract. Eng. Mater. Struct. 21 (1998) 611-630.
14. D. Fridline, Finite element modeling of electromigration and stress voiding in microelectronic interconnects, Ph.D. Thesis, Brown University, 2001.
15. J. Wilkening, L. Borucki, J.A. Sethian, Analysis of stress driven grain boundary diffusion, SIAM J. Appl. Math (submitted).
16. J. Wilkening, Mathematical analysis and numerical simulation of electromigration, Ph.D. Thesis, University of California, Berkeley, May, 2002.
17. J. Wilkening, Extended first order system least squares finite elements for plane elasticity, J. Comput. Phys. (in preparation).
18. M. Berndt, Adaptive refinement and the treatment of discontinuous coefficients for multilevel first-order system least squares (FOSLS), Ph.D. Thesis, University of Colorado at Boulder, 1999.
19. Z. Cai, T.A. Manteuffel, S.F. McCormick, First-order system least squares for second-order partial differential equations: Part II, SIAM J. Numer. Anal. 34 (2) (1997) 425-454.
20. Z. Cai, T.A. Manteuffel, S.F. McCormick, First-order system least squares for the Stokes equations, with application to linear elasticity, SIAM J. Numer. Anal. 34 (5) (1997) 1727-1741.
21. C. Daux, N. Moes, J. Dolbow, N. Sukumar, T. Belytschko, Arbitrary branched and intersecting cracks with the extended finite element method, Int. J. Numer. Meth. Eng. 48 (2000) 1741-1760.
22. L.D. Landau, E.M. Lifshitz, Theory of Elasticity, third ed., Butterworth-Heinemann, Oxford, 1986.
23. P.G. Ciarlet, in: Mathematical Elasticity, vol. 1, North-Holland, Amsterdam, 1993.
24. I.A. Blech, C. Herring, Stress generation by electromigration, Appl. Phys. Lett. 29 (3) (1976) 131-133.
25. E. Hille, R.S. Phillips, Functional Analysis and Semi-groups, American Mathematical Society, Providence, RI, 1957.
26. K. Yosida, Functional Analysis, Springer, Heidelberg, 1980.
27. I.C. Gohberg, M.G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators, Translations of Mathematical Monographs, vol. 18, American Mathematical Society, Providence, RI, 1969.
28. B.A. Plamenevskij, Elliptic boundary value problems in domains with piecewise smooth boundary, in: M.S. Agranovich, Y.V. Egorov, M.A. Shubin (Eds.), Partial Differential Equations IX, Encyclopaedia of Mathematical Sciences, vol. 79, Springer, Berlin, 1997.
29. P. Grisvard, Singularities in Boundary Value Problems, Research Notes in Applied Mathematics, vol. 22, Masson, Paris, 1992.
30. M. Costabel, M. Dauge, Y. Lafranche, Fast semi-analytic computation of elastic edge singularities, Comput. Meth. Appl. Mech. Eng. 190 (2001) 2111-2134.
31. S.I. Larimore, An approximate minimum degree column ordering algorithm (COLAMD/SYMAMD), Master's Thesis, University of Florida, 1998.
32. L.P. Franca, T.J. Hughes, Two classes of mixed finite element methods, Comput. Meth. Appl. Mech. Eng. 69 (1988) 89-129.
33. D. Braess, Finite Elements - Theory, Fast Solvers, and Applications in Solid Mechanics, Cambridge University Press, Cambridge, 1997.